THE AIM AND ACHIEVEMENTS OF SCIENTIFIC METHOD. 119 



same time. For example, the part of the kinetic energy of 

 a small sphere which is due to its velocity is affected, not 

 merely by its mass but also by the electric charge which it may 

 bear, the effect being the same as if its mass were increased. 

 At the same time the presence of the charge adds an indepen- 

 dent term to the expression of the energy. Applying to this 

 expression the operations prescribed by Lagraiige's equation 

 regarding the electric charge as the variable it is easy to 

 deduce the value of a quantity which must bear the same 

 relation to the energy due to the electric charge as ordinary 

 force does to ordinary kinetic energy. 



By an extension of its original meaning, based upon this 

 analogy, and parallel to the extension of the meaning of the 

 term " co-ordinate," we may call any such quantity a " force " 

 of a special " type," determined by the particular co-ordinate 

 with regard to which* the differentiations have been per- 

 formed. In this case the force will be an " electro-motive 

 force," which will involve the velocity of the sphere. But this 

 result implies that the "electrical capacity" of a moving 

 sphere is different from that of the same sphere at rest, a 

 result which before was unknown.f Thus from the known 

 presence of a certain term in the formula for the energy, 

 a term which expressed a known connection between two 

 phenomena the amount of the electrical charge on a moving 

 body and its apparent mass we have been able to deduce 

 a reciprocal effect previously unknown. 



It is important to notice that in Professor Thomson's 

 equations the energy is always expressed as a quadratic 

 function of the co-ordinates or their rates of change. It 

 follows that the " generalized forces " which are obtained by 

 Lagrange's method contain either second differential coefficients 

 analogous to acceleration, or else quantities analogous to 



* And its differential coefficient with respect to the time, 

 t Thomson, op. cit., pp. 31-4. 



